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It has been found that the latencies of recognition significantly and considerably increase if a greater part of a figure is masked.
      
The latter figure ensures the minimum energy output time.
      
This communication deals with a new class of donors that can be used either as external donors in combination with phthalates (A) or as internal/external donors (B).[Figure not available: see fulltext.]
      
For any integers, k and n, 0>amp;lt;k>amp;lt;n, a lower bound for[Figure not available: see fulltext.] is obtained and the exact value is given for 0>amp;lt;k>amp;lt;n≤5.
      
We prove the existence of a linear continuous operator π which is the right inverse of[Figure not available: see fulltext.].
      
Let the self-adjoint operator A and the bounded operator B be specified in Hilbert space ? We let[Figure not available: see fulltext.] denote the spectral family of the operator A.
      
Markushevich obtained the following representation of a function in its holomorphicity star with a sequence {mv}, for which mv+1/mv→∞:[Figure not available: see fulltext.] Here it is proved that this condition is necessary; more precisely,
      
Conditions are derived under which[Figure not available: see fulltext.] is finite or infinite.
      
Under certain conditions on λn >amp;gt; 0 and ?n(x) such as the condition[Figure not available: see fulltext.], we obtain a bound for the coefficients of the polynomial P(x)=#x2211;cnfn(x) in terms of ∥P(x)∥Lp[a,b].
      
For Stechkin's problem of the best approximation for the differentiation operator[Figure not available: see fulltext.] we indicate the necessary and sufficient conditions that En be finite.
      
We prove convergence almost everywhere on [0, 2π] × [0, 2π] of the double Fourier series of functionsf(x, y) with modulus of continuity[Figure not available: see fulltext.] for ?>amp;gt;0.
      
The number[Figure not available: see fulltext.] is called the characteristic of the set M.
      
It is shown that for the Gaussian sums[Figure not available: see fulltext.] the following estimate holds uniformly with respect to all parameters:
      
Deviation of the centroid of a convex figure from the center of the circumscribed disk
      
The estimateOG/R ≤ const ≈ 0.4278 for the distanceOG between the centroid G of a plane closed convex figure and the centerO of its circumscribed disk of radius R is obtained.
      
A class of matrix-valued functions is picked out, invariant relative to the operator[Figure not available: see fulltext.], where t=(t1, ..., tn) are complex variables, x is a real parameter, A(x) is a matrix, {λi(x)}1n=σ(A(x)).
      
It is shown that if f(z) satisfies the equation ML(f)=0, then the expansion coefficients[Figure not available: see fulltext.] rapidly tend to zero.
      
An analog of the Tate hypothesis on homomorphisms of Abelian varieties is proved, in which points of sufficiently large prime order figure in place of the Tate modules.
      
It is shown that for an arbitrary ε >amp;gt; 0 we have[Figure not available: see fulltext.],
      
The best approximation[Figure not available: see fulltext.] [in the space L2(Ω)] of a function f, satisfying a Lipschitz condition with exponent α, 0?α?1, with the aid of certain spaces of local functions, dependent on a parameter h, is discussed.
      
 

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